What is the way to create a texture map?

Once a texture map is generated by the anima‐ tion software, the animator has to painstakingly tweak the unwrapped mesh (the 2D mesh obtained from parameter‐ izing the input 3D model) on the texture plane to align its corresponding features to the 3D model.

What is the key problem in the analysis of the time complexity?

In addi‐ tion, the analysis of the time complexity indicates that running time could rapidly increase when adding a num‐ ber of constraint vertices.

What is the purpose of the embedding?

This embedding is computed to minimize distortion between the 3D mesh and the 2D mapping in order to obtain visually pleasing results.

How many iterations is necessary to compute the itera tive step lengths?

Furthermore, considering the trian‐ gle subdivision procedure, computing the estimated itera‐ tive step lengths using Eq. (6) at every iteration is neces‐ sary.

What is the way to create a 3D texture map?

Without consideration of any internal constraints, a 3D surface can be embedded into a 2D parameterization do‐ main using existing approaches, such as harmonic map‐ ping [16].

What is the iterative step length of Eq. (6)?

Before proceeding further, the iterative step length δ of Eq. (6) is taken as an estimate of the lower bound for our purpose of foldover‐free reparameterization.

How did Kraevoy et al. remove foldovers?

Kraevoy et al. [3] failed to completely remove foldovers because the consistent neighboring ordering was not con‐ sidered in finding matching triangulations.

Open AccessJournal Article10.1109/TVCG.2011.117

An RBF-Based Reparameterization Method for Constrained Texture Mapping

Hongchuan Yu, +5 more

- 01 Jul 2012

- IEEE Transactions on Visualization and C...

- Vol. 18, Iss: 7, pp 1115-1124

TL;DR: The proposed method can reparameterize 2D embedding into a foldover-free 2D mesh, satisfying a set of user-specified constraint points, and generating smooth texture mapping results is possible without extra smoothing optimization.

Abstract: Texture mapping has long been used in computer graphics to enhance the realism of virtual scenes. However, to match the 3D model feature points with the corresponding pixels in a texture image, surface parameterization must satisfy specific positional constraints. However, despite numerous research efforts, the construction of a mathematically robust, foldover-free parameterization that is subject to positional constraints continues to be a challenge. In the present paper, this foldover problem is addressed by developing radial basis function (RBF)-based reparameterization. Given initial 2D embedding of a 3D surface, the proposed method can reparameterize 2D embedding into a foldover-free 2D mesh, satisfying a set of user-specified constraint points. In addition, this approach is mesh free. Therefore, generating smooth texture mapping results is possible without extra smoothing optimization.

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Most frequently asked questions

1. What have the authors contributed in "Rbf-based reparameterization method for constrained texture mapping" ?

In this paper, a radial basis function ( RBF ) based reparameterization is proposed to avoid foldover by adding user-specified positional constraints.

2. What is the main idea behind the use of 3D texture mapping?

Existing research has largely concentrated on producing planar parameterization [1–7] to embed a 3D mesh into a 2D texture space.

3. What is the main computation cost of the proposed method?

The main computation cost, 3(2 )O M , is to de‐ termine the inverse of a real symmetric matrix, where M is the number of the constraint points.

4. What is the main advantage of the RBF scheme?

RBF ensures a smooth final parame‐ terization due to its numerous excellent properties, such as being mesh‐free and C2 continuity.

Figure 3. Illustration of convergence in an extreme case: a) the initial configuration of constraint points; b) the result without triangle subdivision; c) the intermediate result of rotating displacement vectors; d) the final result using triangle subdivision and displacement rotation; and e) the zoomed-in image corresponding to the selected region.

Citations

•Journal Article•10.1145/2461912.2462014

Integer-grid maps for reliable quad meshing

David Bommes, +4 more

- 21 Jul 2013

TL;DR: A novel convex Mixed-Integer Quadratic Programming (MIQP) formulation which ensures by construction that the resulting map is within the class of so called Integer-Grid Maps that are guaranteed to imply a quad mesh.

...read moreread less

235

Journal Article•10.1111/CGF.12452

Remeshing-assisted optimization for locally injective mappings

Yao Jin, +2 more

- 09 Jul 2014

TL;DR: This work proposes to integrate adaptive remeshing into interior point method to solve the issue of locally injective mappings for 2D triangular meshes, and shows that the method has better performance than the solely geometric optimization approaches, especially for extreme deformations.

...read moreread less

•Book

Quad Layouts: Generation and Optimization of Conforming Quadrilateral Surface Partitions 1

Marcel Campen

- 18 Mar 2015

TL;DR: This thesis investigates the structure of the problem and the commonly relevant quality criteria and develops novel efficient solution strategies and algorithms for the generation of high quality quad layouts, and presents a fully automatic as well as an interactive pipeline for this task.

...read moreread less

A fast and simple stretch-minimizing mesh parameterization

Shin Yoshizawa, +4 more

- 01 Jan 2004

TL;DR: In this article, the authors proposed a fast and simple method for generating a low-stretch mesh parameterization, where they start from the floater shape preserving parameterization and then improve the parameterization gradually.

...read moreread less

Journal Article•10.1016/J.GMOD.2013.11.001

Content-aware texture mapping

Yao Jin, +4 more

- 01 May 2014

- Graphical Models \/graphical Models and ...

TL;DR: This work presents a texture mapping method guided by importance map to preserve the shape of the prominent content as an importance-value-weighted parameterization to demonstrate the content-aware effect by comparison to traditional parameterization.

...read moreread less

...

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References

Proceedings Article•10.1145/383259.383266

Reconstruction and representation of 3D objects with radial basis functions

J. C. Carr, +6 more

- 01 Aug 2001

TL;DR: It is shown that the RBF representation has advantages for mesh simplification and remeshing applications, and a greedy algorithm in the fitting process reduces the number of RBF centers required to represent a surface and results in significant compression and further computational advantages.

...read moreread less

2.1K

•Proceedings Article•10.1145/218380.218440

Multiresolution analysis of arbitrary meshes

Matthias Eck, +5 more

- 15 Sep 1995

TL;DR: A method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form, is presented, based on the approximation of an arbitrary initial mesh M by a mesh MJ that has subdivision connectivity and is guaranteed to be within a specified tolerance.

...read moreread less

1.4K

•Proceedings Article•10.1145/566570.566590

Least squares conformal maps for automatic texture atlas generation

Bruno Levy, +3 more

- 01 Jul 2002

TL;DR: This paper introduces a new quasi-conformal parameterization method, based on a least-squares approximation of the Cauchy-Riemann equations, which can parameterize large charts with complex borders, and introduces segmentation methods to decompose the model into charts with natural shapes, and a new packing algorithm to gather them in texture space.

...read moreread less

1.3K

Book Chapter•10.1007/3-540-26808-1_9

Surface Parameterization: a Tutorial and Survey

Michael S. Floater, +1 more

- 01 Jan 2005

TL;DR: Various concepts from differential geometry which are relevant to surface mapping are gathered and used to understand the strengths and weaknesses of the many methods for parameterizing piecewise linear surfaces and their relationship to one another.

...read moreread less

1.1K

Journal Article•10.1016/S0167-8396(96)00031-3

Parametrization and smooth approximation of surface triangulations

Michael S. Floater

- 01 Apr 1997

- Computer Aided Geometric Design

TL;DR: A method based on graph theory is investigated for creating global parametrizations for surface triangulations for the purpose of smooth surface fitting and a particularparametrization, called shape-preserving, is found to lead to visually smooth surface approximations.

...read moreread less

870

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An RBF-Based Reparameterization Method for Constrained Texture Mapping

Chat with Paper

AI Agents for this Paper

Most frequently asked questions

1. What have the authors contributed in "Rbf-based reparameterization method for constrained texture mapping" ?

2. What is the main idea behind the use of 3D texture mapping?

3. What is the main computation cost of the proposed method?

4. What is the main advantage of the RBF scheme?

5. What is the way to create a texture map?

6. What is the key problem in the analysis of the time complexity?

7. What is the purpose of the embedding?

8. How many iterations is necessary to compute the itera tive step lengths?

9. What is the way to create a 3D texture map?

10. What is the iterative step length of Eq. (6)?

11. How did Kraevoy et al. remove foldovers?

Figures

Citations

Integer-grid maps for reliable quad meshing

Remeshing-assisted optimization for locally injective mappings

Quad Layouts: Generation and Optimization of Conforming Quadrilateral Surface Partitions 1

A fast and simple stretch-minimizing mesh parameterization

Content-aware texture mapping

References

Reconstruction and representation of 3D objects with radial basis functions

Multiresolution analysis of arbitrary meshes

Least squares conformal maps for automatic texture atlas generation

Surface Parameterization: a Tutorial and Survey

Parametrization and smooth approximation of surface triangulations

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